Kính mời quý thầy cô, nghiên cứu sinh, học viên cao học các sinh viên quan tâm sắp xếp thời gian đến tham dự buổi seminar Lý thuyết Tối ưu với nội dung sau:
Báo cáo : General versions of the Ekeland variational principle and the Simon satisficing principle.
Người trình bày: NCS. Lê Phước Hải (Đại học Khoa học Tự nhiên TPHCM)
Thời gian: Chủ nhật - 02.06.2019 - 09h30
Địa điểm: phòng F.304 - ĐH Khoa học Tự nhiên, 227 Nguyễn Văn Cừ, Quận 5, TpHCM
Abstract: We prove new general versions of the Ekeland variational principle in a partial quasi-metric space. Unlike the existing versions of this principle, besides a perturbation in terms of the partial quasi-metric, another perturbation being a distance-like bifunction is involved. The classical assumptions on lower semicontinuity of the function and completeness of the space are slightly weakened. The proof technique is new, based onshowing the existence of so-called Ekeland points, which are defined through these two perturbations. Then, we show how these new versions provide striking models for satisficing processes where agents, at each period, do not optimize, but, instead, searchand satisfice. Our new versions of the Ekeland variational principle then are used to develop the Simon satisficing principle which advocates that agents set a satisficing threshold level and search for an alternative until it exceeds this given threshold level. Using a recent variational rationality approach of human dynamics, these new versionsof the Ekeland vatiational principle show the existence of variational traps, such that, starting from an initial position, an agent can satisfice in a worthwhile way, and, being there, is unable to satisfice again in a worthwhile way, giving the end of satisficing process. Moreover, the variatonal approach shows that the Ekeland points represent variational traps (at the intersection of two remarkable sets), which appear to be a set of worthwhile moves starting from the initial point and a set of potential ends (stationary traps).